The Lieb-Thirring inequality for interacting systems in strong-coupling limit

TL;DR

This paper investigates a Lieb-Thirring inequality analogue for interacting quantum systems in the strong-coupling limit, showing convergence of the constant to the one-body Gagliardo-Nirenberg inequality's optimal value.

Contribution

It establishes the behavior of the Lieb-Thirring constant for systems with repulsive interactions in the strong-coupling limit, without requiring wave function antisymmetry.

Findings

Lieb-Thirring constant converges to the Gagliardo-Nirenberg constant in the strong-coupling limit.

The inequality applies to systems with homogeneous repulsive interactions.

Wave function antisymmetry is not assumed in this analysis.

Abstract

We consider an analogue of the Lieb-Thirring inequality for quantum systems with homogeneous repulsive interaction potentials, but without the antisymmetry assumption on the wave functions. We show that in the strong-coupling limit, the Lieb-Thirring constant converges to the optimal constant of the one-body Gagliardo-Nirenberg interpolation inequality without interaction.